Short description

Dirac points are among the most iconic features of modern condensed-matter and photonic physics, underpinning a wide range of topological and transport phenomena. Dirac points lead to the formation of relativistic Landau levels when a magnetic field is applied, and recent studies have shown that closely related effects emerge also in artificial lattice systems through controlled spatial modulations, even in the absence of real magnetic fields.

The Harper–Hofstadter model describes particles on a square lattice subject to an effective magnetic flux per plaquette. This model hosts a remarkably rich band structure with nontrivial topology and, for suitable parameters, Dirac-cone–like features.

This theoretical project explores how spatial modulations and dissipative effects modify the physics of Dirac points and their associated relativistic Landau quantization, and how these features connect to the topology of lattice band structures. The role of non-Hermitian terms, describing gain and loss in photonics, is also investigated, leading to complex spectra and the emergence of exceptional points.

Background

  • Quantum mechanics and linear algebra
  • Basic solid-state or condensed-matter physics
  • Familiarity with tight-binding models
  • Introductory notions of topology (useful but not required)

What you will learn

  • Understand the physical origin of Dirac points in lattice models
  • Analyze Landau-level formation in artificial lattice systems
  • Work with non-Hermitian Hamiltonians and complex energy spectra
  • Explore exceptional points and their physical implications
  • Combine analytical reasoning with numerical simulations in theoretical physics

Interested?

Feel free to contact me for more information.